Question

A body has its centre of mass at the origin. the x-coordinates of the particles
(a) may be all positive
(b) may be all negative
(c) may be all non-negative
(d) may be positive for some cases and negative in other cases.

Answer 1

(c) may be all non-negative
(d) may be positive for some cases and negative for other cases

According to the question, the centre of mass is at origin.

$\therefore$ $X=\frac{m_1{x}_1+m_2{x}_2+m_3{x}_3+...}{m_1+m_2+m_3+.......}=0$
$\Rightarrow m_1{x}_1+m_2{x}_2+m_3{x}_3+...=0$

From the above equation, it can be concluded that all the x-coordinates may be non-negative.

In other words, they may be positive for some cases and negative for others.